Is $1=1$ tautology?

Question

Is "1=1" tautology ?

In this case, "1" means multiplicative identity of real number.

If we treat "1=1" as a simple proposition p , we will get p is not tautology.

But p is always true because it denotes "1=1" which is always true

Can we say that "1=1" is tautology?

Answer 1

See tautology (logic) :

"In logic, a tautology is a formula or assertion that is true in every possible interpretation. A formula of propositional logic is a tautology if the formula itself is always true regardless of which valuation is used for the propositional variables."

Thus, we have two possible readings: the narrow one, restricting the use of the term to propositional logic, and the wider one, regarding logic in general.

According to the wider reading, it is a tautology, because it is an instance of the valid first-order logic formula: $x=x$.